
where the elements of \(\mathbf {\Delta }_t\)  and \(\phi _t\)  are bounded from -1 to 1 and are considered the actions that can be applied to the environment.
The \(\eta \)  term is critical to ensuring effective transfer of policies from the simulation to the real robot.
On the dVRK, joint level control utilized [1]}, so every new end-effector position gives new set points for the joint angles through inverse kinematics.
This means overshoot or even instability can occur if the difference between the new set point and current joint angle is too great.
By choosing a value for \(\eta \)  that ensures negligible overshoot and no instability on the real robot, no dynamics are required for the simulation of the PSM arm, which significantly speeds up the simulation time.
Furthermore, prior work has shown the difficulty in modelling the dynamics of the PSM arm [2]}, [3]}, and using the dynamics would require a separate model for each real PSM arm.
